3.7) For a long time period, if a watershed receives 300 mm of
precipitation and has a 200 mm evapotranspiration annually,
determine annual average runofff.

Answer:

\(y = 3\)

Step-by-step explanation:

Given

Trip = 250 miles

Speed for first x hours = 60 miles/hour

Speed for next y hours = 50 miles/hour

x = 1

Required

Find y

To solve this question, we'll make use of:

\(Distance = Speed * Time\)

For x hours:

\(Distance = 60miles/hour * x\)

Substitute 1 hour for x

\(Distance = 60\ miles/hour * 1\hour\)

\(Distance = 60\ mile\)

For y hours:

\(Distance = 50\ miles/hour * y\ hours\)

\(Distance = 50y\ miles\)

Given that total distance is 210 miles;

We have that:

\(Total Distance = 60\ miles + 50y\ miles\)

\(210\ miles = 60\ miles + 50y\ miles\)

Solve for y

\(210 - 60 = 50y\)

\(150 = 50y\)

\(y = \frac{150}{50}\)

\(y = 3\)

Hence,

y = 3 hours

The area of the new rectangle will be 25 times that of the original

A rectangle is a 2D shape that has 4 sides and equal interior angles

If rectangle has a width of 2.45 feet and a length of 6.5 feet, then;

Width = 2.45 feet

Length = 6.5feet

A = 2.45 * 6.5

A = 15.925 square feet

If each side of the rectangle is increased by a factor of 5, hence;

W1 = 5(2.45) = 12.25feet

L1 = 5(6.5) = 32.5 feet

Determine the area of the new rectangle

A = 12.25 * 32.5

A = 398.125 square feet

Ratio of the area

A1/A = 398.125/15.925

A1 = 25A

Hence the area of the new rectangle will be 25 times that of the original

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Answer:

The ordered pairs that are solution to this equation are:

(8,1) and (10,3)

Step-by-step explanation:

Given statement is:

"difference of two variables x and y is 7"

This can be mathematically written as:

\(x-y = 7\)

To solve this we have to put y = 1 and y = 3

Now,

Putting y = 1 in the equation

\(x-1 = 7\\x = 8\)

Putting y = 3 in the equation

\(x-3 = 7\\x = 7+3\\x = 10\)

Ordered pairs are of the form (x,y)

Hence,

The ordered pairs that are solution to this equation are:

(8,1) and (10,3)

Answer: 3, 323 metric tons

Step-by-step explanation:

Answer:

The height of the taller building is: 51.345m

Step-by-step explanation:

Given

The question has missing details (See attachment for the illustration of the complete question)

Required

The height of the tall building

The height, a, is calculated as:

\(a = b +c\)

To solve for b, we consider the upper half of the attached image

The upper half is a right triangle.

Using tan formula, we have:

\(tan(31) = \frac{b}{30}\)

Solve for b

\(b = 30 * tan(31)\)

To solve for c, we consider the lower half of the attached image

Using tan formula, we have:

\(tan(48) = \frac{c}{30}\)

Solve for c

\(c = 30 * tan(48)\)

Recall that: \(a = b +c\)

So:

\(a = 30 * tan(31) + 30 * tan(48)\)

\(a = 30 * 0.6009 + 30 * 1.1106\)

\(a = 18.027 + 33.318\)

\(a = 51.345\)

Answer:

60

would be right

Step-by-step explanation:

Total length of cable required is 466.18 m.

Pythagoras theorem states that In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.

According to the question

A 100m mast is supported by six cables in two sets of three cables.

They are anchored to the ground at an equal distance from the mast.

The top set of three cables is attached at a point 20m below the top of the mast.

Each cable in the lower set of three cables is 60m long and is attached at a height of 30m above the ground.

One set of guy wires (1 upper and one lower have two right triangles which can solve

The lower right triangle

a = distance from the pole to guy tie point

b = 30 m

c = 60 m the lower guy wire (the hypotenuse)

Using Pythagoras theorem

\(a^{2} +30^{2} =60^{2}\)

⇒ \(a^{2} = 3600 - 900\)

⇒ \(a^{2} =2700\)

⇒ \(a = \sqrt{2700}\)

⇒ \(a = 51.96\) m from the pole to the tie point.

The other triangle using upper guy wire as the hypotenuse (h) tied to a point on the pole 80 m from the ground (20 m from the top) and also 50m from the tie point.

Using Pythagoras theorem

\(h^{2} =(51.96)^{2} +80^{2}\)

⇒ \(h^{2}=2700+6400\)

⇒ \(h^{2}=9100\)

⇒ \(h = \sqrt{9100}\)

⇒ \(h = 95.39\) m , the length of the upper guy wire

For one set of guy wires (1 upper & 1 lower):

= 95.39 + 60

= 155.39 m

For 3 sets of guy wires :

= 3(155.39)

= 466.18 m of wire required

Hence, total length of cable required is 466.18 m.

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Answer:

7 bracelets

Step-by-step explanation:

to find the answer to the question you need to divide the total amount of string by the amount of string needed for each bracelet.

170.1/24.3=7

Answer:

the answer u have is right cause i have telepathy

Step-by-step explanation:

Answer:

D because you add the top and bottom then multiply height. Then divide by 2

Step-by-step explanation:

Answer:

g( \(\frac{3}{2}\) ) = - \(\frac{35}{4}\)

Step-by-step explanation:

substitute x = \(\frac{3}{2}\) into g(x) , that is

g( \(\frac{3}{2}\) )

= - 2( \(\frac{3}{2}\) )³ - \(\frac{4}{3}\) × \(\frac{3}{2}\)

= - 2 × \(\frac{27}{8}\) - 2

= = - \(\frac{27}{4}\) - \(\frac{8}{4}\)

= - \(\frac{35}{4}\)

There are 5 full square and 6 triangles that are half squares.

      5 + (6)(1/2) = 5 + 3 = 8

You could also break this into smaller shapes (like a big triangle on the top and a smaller triangle and rectangle on the bottom and use area formulas to calculate the area.  But counting works well in this example.

Answer: 8

Step-by-step explanation:

First you split up this shape into two different shapes, a triangle and trapezoid

Put a line through the coordinates (-2,2) to  (-1,2); the top is a triangle and the other is a trapezoid

Area of the trapezoid is A = .5x (base1 + base2) x height

base1 of the trapezoid goes from -4 to -1 which is 3

base2 goes from -2 to -1 which is 1

height is 0 to 2 whcich is 2

A = .5 x (3+1) x 2 = 4

Now area of a triangle is A = .5 x base x height

the base goes from -2 to 2 which is 4

the height goes from 2 to 4 which is 2

A = .5 x (4) x (2) = 4

Area of the Trapezoid + Area of the Triangle = Total Area

4 + 4 = 8

The juice can will have a minimum material used if the radius of the cylinder is  1.8533 in and the height is 3.7069 in.

Let the radius of the cylindrical can be r in

We are given that the can holds 40 in³ of juice

Hence from the formula of cylinder, we have

πr² X height = 40

or, height = 40/πr²

The total surface area of a cylinder is given by

2π X radius X height + 2π X (radius)²

= 2πr X 40/πr²  +  2πr²

= 80/r  +  2πr²

Now we need to minimize the above equation

Hence differentiating with respect to r and equating to 0 we get

-80/r² + 4πr = 0

or, -20/r² + πr = 0

or, -20 + πr³ = 0

or, r³ = 20/π

or, r = ∛(20/π)

or, r = 1.8533

Now differentiating again with respect to r we get

160/r³ + 4π

Putting r = ∛(20/π) gives us

8π + 4π = 12π

Since the above result is positive, r = 1.8533 in is the value of the radius for which the surface area is minimized

Hence height is 3.7069 in

Hence the juice can will have a minimum material used if the radius of the cylinder is  1.8533 in and height is 3.7069 in.

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Correct Question

(Image Attached)

Answer:

$27.32 × .15 = $4.10 tip

$27.32 + $4.10 = $31.42 total

Mark should pay $31.42.

Answer:

27.7 is the answer.

Step-by-step explanation:

The combined length would be adding. Add 12.45+2.8+12.45

The point that is equidistant of the points (7, 3) and (13, -1) is (3.33, -9)

Remember the distance between two points (x₁, y₁) and (x₂, y₂) can be written as:

distance = √( (x₂ - x₁)² + ( y₂ -  y₁)²)

We want to find a point (x, y), that lies on the line y = -9 that is equidistant to  (7, 3) and (13, -1)

We can rewrite our point as (x, -9)

And the distances to the given points are:

distance = √( (x - 7)² + ( -9 - 3)²)

distance = √( (x - 13)² + ( -9 + 1)²)

These distances must be equal, (that is what equidistant means) so we can write:

√( (x - 7)² + ( -9 - 3)²) = √( (x - 13)² + ( -9 + 1)²)

Now we can remove the square root and simplify the equation:

(x - 7)² + ( -9 - 3)² =  (x - 13)² + ( -9 + 1)²

(x - 7)² + 144 = (x - 13)² + 64

x^2 - 14x + 49 + 144 = x^2 - 26x + 169 + 64

-14x + 26x = 169 + 64 - 49 - 144

12x = 40

x = 40/12

x = 3.33

The point is (3.33, -9)

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If an angle is acute, then its supplement is an obtuse angle (true).

An acute angle is an angle that has a measurement that is below 90 degrees (right angle).

The measurement of an obtuse angle is less than 180 degrees but more than angle 90 degrees (right angle).

The supplement of an angle is the measure of that angle subtracted from 180 degrees.

For example, if an acute angle measures 30°, therefore:

The complement of 30° = 90 - 30 = 60°. 60° is also an acute angle.

The supplement of 30° = 180 - 30 = 150°. 150° is an obtuse angle.

Therefore, we can conclude that: if an angle is acute, then its supplement is an obtuse angle (true).

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To determine Bob's expected utility for each option, we calculate the utility for each outcome and weigh them by their respective probabilities.

Option A:

Expected utility = 0.5v(316 - 30) + 0.5v(4 - 0)

= 0.5v(48) + 0.5v(4) = 0.548 + 0.54 = 26.

Option B: Expected utility = v(8) = 8.  

Bob would choose Option A as it has a higher expected utility.

ii. Option A: Expected utility = 0.5v(-16) + 0.5v(-4) = 0.5*(-32) + 0.5*(-8)

= -20.

Option B: Expected utility = v(-12) = -24. Bob would choose Option B as it has a higher expected utility.

iii. Option A: Expected utility = 0.5v(8) + 0.5v(-4) = 0.58 + 0.5(-8) = 0. Option B: Expected utility = v(1) = 1.  Bob would choose Option B as it has a higher expected utility.

 (b) If Bob buys the hammer for $2, his utility would be v(-2) = -4. If he does not buy the hammer, his utility would be v(0) = 0. Bob would prefer not to buy the hammer since the utility is higher at 0.

(c) If Bob sells the hammer for $2, his utility would be v(2) = 2. If he does not sell the hammer, his utility would be v(0) = 0. Bob would prefer to sell the hammer since the utility is higher at 2. (d) Bob's buying price is not the same as his selling price.

This concept is known as loss aversion, where individuals tend to value losses more than equivalent gains. One study that demonstrates a similar concept is the "Prospect Theory" by Daniel Kahneman and Amos Tversky, which shows how people's decision-making is influenced by the potential for gains and losses and how they weigh them differently.

The study revealed that individuals are generally more averse to losses and are willing to take greater risks to avoid losses compared to the risks they are willing to take for potential gains of equal value.

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Answer:

142.5

Step-by-step explanation:

9,500 x .015 = 142.5

Answer:

next 3 terms are 17,20,23

Step-by-step explanation:

to get from 5 to 8 you add 3

14+3=17

17+3=20

20+3=23

Answer:

17, 20, 23

Step-by-step explanation:

The pattern is that 3 is added every time.

5 + 3 = 8, 8 + 3 = 11, 11 + 3 = 14.

That means that the next terms will be

14 + 3 = 17

17 + 3 = 20

20 + 3 = 23

56.6 years  is the mean of the modes of the given set of numbers.

What are the mean, median, and example?

The most frequent number, or the one that happens the most frequently, is known as the mode.

                     Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.

The mean is calculated by adding together all the values

                 =  (54+54+54+55+56+57+57+58+58+60+60

                  = 623

                  =  56.6 years.

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Answer:

if 312four + 52p = 96 find the value of p

The area of the shaded region for the circle is derived to be equal to 63 square units.

The shaded region in the circle comprises of a triangle with base and height 7 units and a sector with 90° angle, hence the area of the shaded region is the sum of the area of the triangle and sector calculated as follows:

area of triangle = 1/2 × 7 units × 7 units

area of triangle = 24.5 square units

area of sector = 90/360 × 22/7 × 7 units × 7 units

area of sector = 38.5 square units

area of the shaded region = 24.5 square units + 38.5 square units

area of the shaded region = 63 square units

Therefore, the area of the shaded region for the circle is derived to be equal to 63 square units.

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No, these two matrices are not equal.

The first matrix is a 3x3 matrix with the elements [[3,-1,7],[2,6,-9],[-5,4,-2]] and the second matrix is also a 3x3 matrix with the elements [[-2,-9,7],[4,6,-1],[-5,2,3]]. In order for two matrices to be equal, they must have the same dimensions and the corresponding elements must be equal. In this case, the dimensions are the same, but the corresponding elements are not equal. For example, the first element in the first matrix is 3, but the first element in the second matrix is -2. Therefore, these two matrices are not equal.

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Answer:

second option, it represents the y-intercept before the rocket is propelled

Step-by-step explanation:

corr(max(x,y),min(x,y)) cannot be equal to corr(x,y) as they are not equivalent. The answer is no.

In statistics, correlation is the degree of association between two random variables. In this case, x and y are independent random variables with nonzero standard deviations. corr(x, y) is the correlation coefficient between x and y and corr(max(x, y), min(x, y)) is the correlation coefficient between the maximum value of x and y and the minimum value of x and y.

Therefore, the answer is no. They cannot be equivalent because the two correlation coefficients refer to different pairs of random variables. The max and min functions convert the original variables into a new pair, so their correlation cannot be the same as the original pair. Hence, corr(max(x,y),min(x,y)) cannot be equal to corr(x,y).

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Answer:

6 miles

Step-by-step explanation:

because the common denominator is 12 so the man will walk 12 miles in 4 hours and the woman will walk 12 miles in 2 hours so they will meet in the middle

If point A and point B are 15 miles apart, they will meet H) 10 miles from point B.

The answer to the question is H: 10 miles.

To solve this problem, we can use the concept of relative velocity. Relative velocity is the velocity of one object as seen by another object. In this case, the man and the woman are moving towards each other, so their relative velocity is the sum of their individual velocities.

The man's velocity is 3 miles per hour and the woman's velocity is 6 miles per hour, so their relative velocity is 3 + 6 = 9 miles per hour.

We know that point A and point B are 15 miles apart, so they will meet when the distance between them is 0. The time it takes them to meet is 15 / 9 = 5/3 hours.

In 5/3 hours, the man will travel 3 * 5/3 = 5 miles and the woman will travel 6 * 5/3 = 10 miles. Therefore, they will meet 10 miles from point B.

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Answer:

it is median

Step-by-step explanation:

because it have number in alphabetic order

The different ways in which she can jump up a set of five steps is: 4 + 3 + 1 = 8 ways.

By choosing some items from a set and creating subsets, permutation and combination are two approaches to represent a group of objects. It outlines the numerous configurations for a particular set of data. Permutations are the selection of data or objects from a set, whereas combinations are the order in which they are represented. Both ideas are critical to mathematics.

Here, the differences between permutation and combination are described in detail.

The given steps are 5.

Thus, we have the following possibilities:

For 1 double step and 3 single steps:

4! / 3! = 4

For 2 double steps and 1 single step:

3! / 2! (1!) = 3

For 5 single steps: 1 way

Thus, the different ways in which she can jump up a set of five steps is:

4 + 3 + 1 = 8 ways.

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Percentage of the time will the number of boxes received weekly be between 180 and 210 is 53.28%..

A Z-score indicates how deviates a particular value from standard deviation. Standard deviation essentially reflects the amount of variability within the data set. Weekly received supplies of boxes in plant organization is normally distributed.

Mean, μ = 200

standard deviation, σ =20

Formula for Z-score is

Z = (sample mean- actual mean)/standard deviation

We have to calculate percentage of the time will the number of boxes received weekly be between 180 and 210.

Z₁ (at 180) = (180 - 200)/20 = -1

z₂(at 210) = (210 - 200)/20 = 0.5

Now, P(-1 < z< 0.5) = P (z<0.5)- P(z<-1)

Using the Z- table, value of P (z<0.5) and p(-1) are 0.158 and 0.6915 respectively. So, P(z<0.5)- P(z<-1) = 0.6915 - 0.158

= 0.5328 = 53.28%

Hence, Probability, P(-1 < z< 0.5) is 0.5328 and in percentage it is 53.28%..

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